Simplify the following expression: $ x = -2 + \dfrac{-5a + 5}{-5a - 7} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5a - 7}{-5a - 7}$ $ \dfrac{-2}{1} \times \dfrac{-5a - 7}{-5a - 7} = \dfrac{10a + 14}{-5a - 7} $ Therefore $ x = \dfrac{10a + 14}{-5a - 7} + \dfrac{-5a + 5}{-5a - 7} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{10a + 14 - 5a + 5}{-5a - 7} $ $x = \dfrac{5a + 19}{-5a - 7}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{-5a - 19}{5a + 7}$